Here's another example of how etymologies are not definitions. Those people who complain when decimate is used to mean something other than "destroy ten percent", or when unique is used to mean something other than "one of a kind", should complain whenever giddy is used to mean something other than "possessed by god".
It's from Old English gidiġ "mad, insane, foolish, stupid", from *gydiġ, an ablauted version of Proto-Germanic *ǥuđīǥo-, which is composed of *ǥuđo- "god" and the suffix *-īǥo-. The OED says the primary meaning is "possessed by a god". If *-īǥo- is English -y as in icy, rainy, dusty etc. then giddy is "goddy" or "full of god".
There is a similar etymology in enthusiasm.
The further etymology of god is disputed. Both the OED and the AHD offer two theories. It might be derived from PIE *ǵhu-tom, the neuter verbal adjective of *ǵheu- "to pour, pour a libation" (Sanskrit hu "to sacrifice", Greek χέω "to pour", Latin fundō "to pour"). Or it could be from *ǵheu(H)- "to call, invoke" (Sanskrit hū "to call"). So it could have the etymological meaning of "what is worshipped by sacrifice" or "what is invoked".